Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

Q: 1 Evaluate: lim sin2(x) 4 TC 6 6.

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Q: c) Use Secant Method to find the root of f(x)= x -x-1 with two initial points x, = 1 and=1.5 and =…

A: Secant method Steps  Step-1: Find points x0 and x1 such that x0<x1 and f(x0)⋅f(x1)<0.…

Q: Which function has vertical asymptotes x =-3 and x = ? Os(2) = а) 1 2x2+7x+3 O® {(2) = = 1 222 —5х—3…

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Q: lim sin(x)d.x (x2 + e2)2

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Q: 1/a | sin(t")dt Find lim T.

A: We have to calculate the value of : limx→∞∫01xsint2dt·x

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A: Find the limit when x tends to 0

Q: tan(sin(ra)) tan(т(»—100)) Find lim

A: The objective is to evaluate the limit.

Q: (7) Lim x= 1/2 X- X COS X TT- 2X

A: Since you have posted multiple questions and we will provide the solution only to the first question…

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: x2-8x+15 ; x 3 a) If f(x)= 2x-6 is continuous at x=3, then find the 2-5 ;x=3 value(s) of k. sinx b)…

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Q: 3e2* -1 d) lim 2x 4e* +cos x

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Q: 1.1288 (x)=: tanh (1.3288V* )using bisection Determine the real root of method to locate the root.…

A: Function: f(x)=1.1288x-tanh1.3288x When x=1 and x=2,…

Q: lim (x' – 2x* +5)= x→-2 O a. 22 O b. -11 O C. -13 O d. -18

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Q: In evaluating 2 2 dx XV is same as evaluating lim_ cos-¹(f(x)). Determine the value of f(x) if x=2.9…

A: As per the question we are given a definite integral and we have to find the primitive of the…

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: (x + h) – x .3 - 31. lim

A: From the given data:

Q: lim x →0 In(1+³) x.sin x²

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Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

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Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: (2) limuy)-(0,0) In(1+x²y®) =,

A: When we put x=0 , y=0 in the function we donot get indeterminant form so we can put the values…

Q: Find x + sin lim r00 x + cos x

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Q: 1-sinx x²-49 b. lim x→7 x-7 lim C. lim X→00 x²+1 a. X 1-cosx

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Q: sin 14x 27. Let L = lim х sin e 14x, that L = lim 14- (a) Show, by letting 0 (b) Compute L.

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Q: lim(log(3x +1)) 2. 3 lim(sin (5x2+ 10) 3. *2

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Q: V3r-1 7. lim X- sin? x-cos(2x)

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Q: 1 1\x (x + sin lim X x→+0 X.

A: Given: limx→∞(x+sin1x)1x

Q: 10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

A: We have to use proper techniques here.

Q: Find the discontinuities, if any.  f(x) = sin (x^2 - 2)  f(x) = sec x lim    sin θ / θ2 θ→0+

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Q: T+tan x 4. lim sin X→0 tan x-2 sec x,

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